Regular matrix transformations and rates of convergence of positive linear operators

Abstract This paper investigates the effects of matrix summability methods on the A-statistical approximation of sequences of positive linear operators defined on the space of all 2π-periodic and continuous functions on the whole real axis. The two main tools used in this paper are A-statistical convergence and the modulus of continuity. Keywords: Regular infinite matrices, A-statistical convergence, rates of A-statistical convergence, positive linear operators, the Korovkin theorem, modulus of continuity. Mathematics Subject Classification (2000): 41A25, 41A36     

Validating and Calibrating Agent-Based Models: A Case Study

In this paper we deal with some validation and calibration experiments on a modified version of the Complex Adaptive Trivial System (CATS) model proposed in Gallegati et al. (2005 Journal of Economic Behavior and Organization, 56, 489–512). The CATS model has been extensively used to replicate a large number of scaling types stylized facts with a remarkable degree of precision. For such purposes, the simulation of the model has been performed entering ad hoc parameter values and using the same initial set up for all the agents involved in the experiments. Nowadays alternative robust and reliable validation techniques for determining whether the simulation model is an acceptable representation of the real system are available. Moreover many distributional and goodness-of-fit tests have been developed while several graphical tools have been proposed to give the researcher a quick comprehension of actual and simulated data. This paper discusses some validation experiments performed with the modified CATS model. In particular starting from a sample of Italian firms included in the CEBI database, we perform several ex-post validation experiments over the simulation period 1982–2000. In the experiments, the model parameters have been estimated using actual data and the initial set up consists of a sample of agents in 1982. The CATS model is then simulated over the period 1982–2000. Using alternative validation techniques, the simulations’ results are ex-post validated with respect to the actual data. The results are promising in that they show the good capabilities of the CATS model in reproducing the observed reality. Finally we have performed a first calibration experiment via indirect inference, in order to ameliorate our estimates. Even in this case, the results are interesting.     

A Multicriteria Weighted Vote‐Based Classifier Ensemble for Heart Disease Prediction

The availability of a large amount of medical data leads to the need of intelligent disease prediction and analysis tools to extract hidden information. A large number of data mining and statistical analysis tools are used for disease prediction. Single data‐mining techniques show acceptable level of accuracy for heart disease diagnosis. This article focuses on prediction and analysis of heart disease using weighted vote‐based classifier ensemble technique. The proposed ensemble model overcomes the limitations of conventional data‐mining techniques by employing the ensemble of five heterogeneous classifiers: naive Bayes, decision tree based on Gini index, decision tree based on information gain, instance‐based learner, and support vector machines. We have used five benchmark heart disease data sets taken from UCI repository. Each data set contains different set of feature space that ultimately leads to the prediction of heart disease. The effectiveness of proposed ensemble classifier is investigated by comparing the performance with different researchers' techniques. Tenfold cross‐validation is used to handle the class imbalance problem. Moreover, confusion matrices and analysis of variance statistics are used to show the prediction results of all classifiers. The experimental results verify that the proposed ensemble classifier can deal with all types of attributes and it has achieved the high diagnosis accuracy of 87.37%, sensitivity of 93.75%, specificity of 92.86%, and F‐measure of 82.17%. The F‐ratio higher than the F‐critical and p‐value less than 0.01 for a 95% confidence interval indicate that the results are statistically significant for all the data sets.     

Quotient convergence and multi-splitting methods for solving singular linear equations

Abstract   In this paper, we use the group inverse to characterize the quotient convergence of an iterative method for solving consistent singular linear systems, when the matrix index equals one. Next, we show that for stationary splitting iterative methods, the convergence and the quotient convergence are equivalent, which was first proved in [7]. Lastly, we propose a (multi-)splitting iterative method A=F–G, where the splitting matrix F may be singular, endowed with group inverse, by using F ^# as a solution tool for any iteration. In this direction, sufficient conditions for the quotient convergence of these methods are given. Then, by using the equivalence between convergence and quotient convergence, the classical convergence of these methods is proved. These latter results generalize Cao’s result, which was given for nonsingular splitting matrices F. Keywords: Group inverse, singular linear equations, iterative method, P-regular splitting, Hermitian positive definite matrix, multi-splitting, quotient convergence AMS Classification: 15A09, 65F35     

Complexity theoretic hardness results for query learning

We investigate the complexity of learning for the well-studied model in which the learning algorithm may ask membership and equivalence queries. While complexity theoretic techniques have previously been used to prove hardness results in various learning models, these techniques typically are not strong enough to use when a learning algorithm may make membership queries. We develop a general technique for proving hardness results for learning with membership and equivalence queries (and for more general query models). We apply the technique to show that, assuming , no polynomial-time membership and (proper) equivalence query algorithms exist for exactly learning read-thrice DNF formulas, unions of halfspaces over the Boolean domain, or some other related classes. Our hardness results are representation dependent, and do not preclude the existence of representation independent algorithms.?The general technique introduces the representation problem for a class F of representations (e.g., formulas), which is naturally associated with the learning problem for F. This problem is related to the structural question of how to characterize functions representable by formulas in F, and is a generalization of standard complexity problems such as Satisfiability. While in general the representation problem is in , we present a theorem demonstrating that for "reasonable" classes F, the existence of a polynomial-time membership and equivalence query algorithm for exactly learning F implies that the representation problem for F is in fact in co-NP. The theorem is applied to prove hardness results such as the ones mentioned above, by showing that the representation problem for specific classes of formulas is NP-hard. Received: December 6, 1994     

Learning bidirectional asymmetric similarity for collaborative filtering via matrix factorization

Memory-based collaborative filtering (CF) aims at predicting the rating of a certain item for a particular user based on the previous ratings from similar users and/or similar items. Previous studies in finding similar users and items have several drawbacks. First, they are based on user-defined similarity measurements, such as Pearson Correlation Coefficient (PCC) or Vector Space Similarity (VSS), which are, for the most part, not adaptive and optimized for specific applications and data. Second, these similarity measures are restricted to symmetric ones such that the similarity between A and B is the same as that for B and A, although symmetry may not always hold in many real world applications. Third, they typically treat the similarity functions between users and functions between items separately. However, in reality, the similarities between users and between items are inter-related. In this paper, we propose a novel unified model for users and items, known as Similarity Learning based Collaborative Filtering (SLCF) , based on a novel adaptive bidirectional asymmetric similarity measurement. Our proposed model automatically learns asymmetric similarities between users and items at the same time through matrix factorization. Theoretical analysis shows that our model is a novel generalization of singular value decomposition (SVD). We show that, once the similarity relation is learned, it can be used flexibly in many ways for rating prediction. To take full advantage of the model, we propose several strategies to make the best use of the proposed similarity function for rating prediction. The similarity can be used either to improve the memory-based approaches or directly in a model based CF approaches. In addition, we also propose an online version of the rating prediction method to incorporate new users and new items. We evaluate SLCF using three benchmark datasets, including MovieLens, EachMovie and Netflix, through which we show that our methods can outperform many state-of-the-art baselines.     

From liveness to promptness

Liveness temporal properties state that something “good” eventually happens, e.g., every request is eventually granted. In Linear Temporal Logic (LTL), there is no a priori bound on the “wait time” for an eventuality to be fulfilled. That is, F θ asserts that θ holds eventually, but there is no bound on the time when θ will hold. This is troubling, as designers tend to interpret an eventuality F θ as an abstraction of a bounded eventuality F ^≤k θ, for an unknown k, and satisfaction of a liveness property is often not acceptable unless we can bound its wait time. We introduce here prompt-LTL, an extension of LTL with the prompt-eventually operator F _p . A system S satisfies a prompt-LTL formula φ if there is some bound k on the wait time for all prompt-eventually subformulas of φ in all computations of S. We study various problems related to prompt-LTL, including realizability, model checking, and assume-guarantee model checking, and show that they can be solved by techniques that are quite close to the standard techniques for LTL.     

Integral-type generalizations of operators obtained from certain multivariate polynomials

Abstract In this work, we mainly focus on the Kantorovich-type (integral-type) generalizations of the positive linear operators obtained from the Chan-Chyan-Srivastava multivariable polynomials. Using the notion of A-statistical convergence, we obtain various approximation theorems including a statistical Korovkin-type result and rates of A-statistical convergence with the help of the modulus of continuity, Lipschitz class functionals and Peetre’s K-functionals. We also introduce an sth order generalization of our approximating operators. Keywords. Chan-Chyan-Srivastava multivariable polynomials, Korovkin approximation theorem, Kantorovich-type operators, A-statistical convergence, modulus of continuity, Lipschitz class functional, Peetre’s K-functional Mathematics Subject Classification (2000): Primary: 41A25; 41A36, Secondary: 33C45     

Experimental evidence of application of direct and inverse operators in complex processes

In this survey we illustrate basic procedures and methods for application of direct and inverse operators on a composite function and for determination of periodicities. We obtain a simplified regularization of the FFT (fast Fourier transform) on a complex process. For that matter, we have introduced a direct (A) and an inverse (A ⁻¹) operator in the FFT and in some other complex processes, where a one-dimensional array serves as an operator. We give some correct theoretical and experimental justification of these operators and discuss a program which uses similar algorithms. We provide experimental results of a complex function after application of direct and inverse operators. Sergey V. Ivanov. Born 1972. Graduated from the St. Petersburg State Electrotechnical University “LETI” (ETU) in 1997. Scientific interests: development of programmatic-algorithmic tools for biomedical investigations and biomedical data processing (mostly psychophysiological) from the viewpoint of games theory and statistical decision theory. Author of more than 25 publications.     

On solving a special class of weakly nonlinear finite-difference systems

In this paper, we consider the Newton-iterative method for solving weakly nonlinear finite-difference systems of the form F ( u )=A u + G ( u )=0, where the jacobian matrix G′( u ) satisfies an affine invariant Lipschitz condition. We also consider a modification of the method for which we can improve the likelihood of convergence from initial approximations that may be outside the attraction ball of the Newton-iterative method. We analyse the convergence of this damped method in the framework of the line search strategy. Numerical experiments on a diffusion–convection problem show the effectiveness of the method.     

Creating a nilpotent pencil via deadbeat

We consider the problem of finding a square low-rank correction (λC ? B)F to a given square pencil (λE ? A) such that the new pencil λ(E ? CF) ? (A ? BF) has all its generalised eigenvalues at the origin. We give necessary and sufficient conditions for this problem to have a solution and we also provide a constructive algorithm to compute F when such a solution exists. We show that this problem is related to the deadbeat control problem of a discrete-time linear system and that an (almost) equivalent formulation is to find a square embedding that has all its finite generalised eigenvalues at the origin.     

Scheduling two agents on uniform parallel machines with makespan and cost functions

We consider the problem of scheduling two jobs A and B on a set of m uniform parallel machines. Each job is assumed to be independent from the other: job A and job B are made up of n _A and n _B operations, respectively. Each operation is defined by its processing time and possibly additional data such as a due date, a weight, etc., and must be processed on a single machine. All machines are uniform, i.e. each machine has its own processing speed. Notice that we consider the special case of equal-size operations, i.e. all operations have the same processing time. The scheduling of operations of job A must be achieved to minimize a general cost function F ^A , whereas it is the makespan that must be minimized when scheduling the operations of job B. These kind of problems are called multiple agent scheduling problems. As we are dealing with two conflicting criteria, we focus on the calculation of strict Pareto optima for F ^A and C_max^BC_{\mathrm{max}}^{B} criteria. In this paper we consider different min-max and min-sum versions of function F ^A and provide special properties as well as polynomial time algorithms.     

A technical characterization of APTs by leveraging public resources

Advanced persistent threats (APTs) have rocketed over the last years. Unfortunately, their technical characterization is incomplete—it is still unclear if they are advanced usages of regular malware or a different form of malware. This is key to develop an effective cyberdefense. To address this issue, in this paper we analyze the techniques and tactics at stake for both regular and APT-linked malware. To enable reproducibility, our approach leverages only publicly available datasets and analysis tools. Our study involves 11,651 regular malware and 4686 APT-linked ones. Results show that both sets are not only statistically different, but can be automatically classified with F1 > 0.8 in most cases. Indeed, 8 tactics reach F1 > 0.9. Beyond the differences in techniques and tactics, our analysis shows thats actors behind APTs exhibit higher technical competence than those from non-APT malwares.

     

Context-aware,self-scaling Fuzzy ArtMap for received signal strength based location systems

Location awareness is the key capability of mobile computing applications. Despite high demand, indoor location technologies have not become truly ubiquitous mainly due to their requirements of costly infrastructure and dedicated hardware components. Received signal strength (RSS) based location systems are poised to realize economical ubiquity as well as sufficient accuracy for variety of applications. Nevertheless high resolution RSS based location awareness requires tedious sensor data collection and training of classifier which lengthens location system development life cycle. We present a rapid development approach based on online and incremental learning method which significantly reduces development time while providing competitive accuracy in comparison with other methods. ConSelFAM (Context-aware, Self-scaling Fuzzy ArtMap) extends the Fuzzy ArtMap neural network system. It enables on the fly expansion and reconstruction of location systems which is not possible in previous systems.     

n-Fold obstinate filters in BL-algebras

In this paper, we introduced the notion of n-fold obstinate filter in BL-algebras and we stated and proved some theorems, which determine the relationship between this notion and other types of n-fold filters in a BL-algebra. We proved that if F is a 1-fold obstinate filter, then A/F is a Boolean algebra. Several characterizations of n-fold fantastic filters are given, and we show that A is a n-fold fantastic BL-algebra if A is a MV-algebra (n ≥ 1) and A is a 1-fold positive implicative BL-algebra if A is a Boolean algebra. Finally, we construct some algorithms for studying the structure of the finite BL-algebras and n-fold filters in finite BL-algebras.     

Affine Approximation for Direct Batch Recovery of Euclidian Structure and Motion from Sparse Data

We present a batch method for recovering Euclidian camera motion from sparse image data. The main purpose of the algorithm is to recover the motion parameters using as much of the available information and as few computational steps as possible. The algorithm thus places itself in the gap between factorisation schemes, which make use of all available information in the initial recovery step, and sequential approaches which are able to handle sparseness in the image data. Euclidian camera matrices are approximated via the affine camera model, thus making the recovery direct in the sense that no intermediate projective reconstruction is made. Using a little known closure constraint, the F_A-closure, we are able to formulate the camera coefficients linearly in the entries of the affine fundamental matrices. The novelty of the presented work is twofold: Firstly the presented formulation allows for a particularly good conditioning of the estimation of the initial motion parameters but also for an unprecedented diversity in the choice of possible regularisation terms. Secondly, the new autocalibration scheme presented here is in practice guaranteed to yield a Least Squares Estimate of the calibration parameters. As a bi-product, the affine camera model is rehabilitated as a useful model for most cameras and scene configurations, e.g. wide angle lenses observing a scene at close range. Experiments on real and synthetic data demonstrate the ability to reconstruct scenes which are very problematic for previous structure from motion techniques due to local ambiguities and error accumulation.     

A framework for software process deployment and evaluation

ContextSoftware Process Engineering promotes the systematic production of software by following a set of well-defined technical and management processes. A comprehensive management of these processes involves the accomplishment of a number of activities such as model design, verification, validation, deployment and evaluation. However, the deployment and evaluation activities need more research efforts in order to achieve greater automation.ObjectiveWith the aim of minimizing the required time to adapt the tools at the beginning of each new project and reducing the complexity of the construction of mechanisms for automated evaluation, the Software Process Deployment & Evaluation Framework (SPDEF) has been elaborated and is described in this paper.MethodThe proposed framework is based on the application of well-known techniques in Software Engineering, such as Model Driven Engineering and Information Integration through Linked Open Data. It comprises a systematic method for the deployment and evaluation, a number of models and relationships between models, and some software tools.ResultsAutomated deployment of the OpenUP methodology is tested through the application of the SPDEF framework and support tools to enable the automated quality assessment of software development or maintenance projects.ConclusionsMaking use of the method and the software components developed in the context of the proposed framework, the alignment between the definition of the processes and the supporting tools is improved, while the existing complexity is reduced when it comes to automating the quality evaluation of software processes.     

Development of process-centered IPSEs in the ALF project

In this article we describe the main results of the ESPRIT project ALF (in French: Accueil de Logiciel Futur or Advanced Software Engineering Environments' Logistics Framework). In ALF we have developed a framework for Integrated Programming Support Environments (IPSEs), a software process modeling language (based on the notion of Models of Assisted Software Processes (MASP)), and an environment used to develop software process models. A MASP describes a software development method. This method specifies how an IPSE should behave. It can be plugged into the framework for IPSEs. Moreover, a MASP is used to integrate tools into the IPSE framework. In this article we focus on assistance and guidance facilities for software developers implemented in the framework for IPSEs.     

线性动态系统反演模型在人体行为识别的应用

目的 人体行为识别在视频监控、环境辅助生活、人机交互和智能驾驶等领域展现出了极其广泛的应用前景。由于目标物体遮挡、视频背景阴影、光照变化、视角变化、多尺度变化、人的衣服和外观变化等问题,使得对视频的处理与分析变得非常困难。为此,本文利用时间序列正反演构造基于张量的线性动态模型,估计模型的参数作为动作序列描述符,构造更加完备的观测矩阵。方法 首先从深度图像提取人体关节点,建立张量形式的人体骨骼正反向序列。然后利用基于张量的线性动态系统和Tucker分解学习参数元组（A_F,A_I,C）,其中C表示人体骨架信息的空间信息,A_F和A_I分别描述正向和反向时间序列的动态性。通过参数元组构造观测矩阵,一个动作就可以表示为观测矩阵的子空间,对应着格拉斯曼流形上的一点。最后通过在格拉斯曼流形上进行字典学习和稀疏编码完成动作识别。结果 实验结果表明,在MSR-Action 3D数据集上,该算法比Eigenjoints算法高13.55%,比局部切从支持向量机（LTBSVM）算法高2.79%,比基于张量的线性动态系统（tLDS）算法高1%。在UT-Kinect数据集上,该算法的行为识别率比LTBSVM算法高5.8%,比tLDS算法高1.3%。结论 通过大量实验评估,验证了基于时间序列正反演构造出来的tLDS模型很好地解决了上述问题,提高了人体动作识别率。